The alpha-parameter is a variable appearing in the formulation of the Bray number, a dimensionless term that can be used to predict the behaviour of the turbulent scalar flux as counter-gradient or gradient in premixed combustion. However, the successful application of the Bray number is hampered by poor characterisation of the alpha-parameter. The results of previous laser-imaging studies of conditional mean velocities in turbulent premixed methane/air and propane/air Bunsen-flames are used to formulate an empirical description of alpha. The resulting description of a suggests that the behaviour of the scalar flux is dependent on the heat release parameter and the lengthscale ratio, iota(I)/delta(L) rather than the velocity ratio, u'/S-L.